Precise numerical results for limit cycles in the quantum three-body problem

The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930s. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems (e.g., few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed.     

Three-body forces in sd-shell nuclei

The influence of three-body forces on the excitation spectra of nuclei with 3 valence nucleons in the sd-shell is investigated. Three-body forces are considered, which arise from an intermediate excitation of the interacting nucleons to the Δ(3, 3) resonance. Besides these real three-nucleon forces, effective three-body interactions are taken into account which are due to the restriction of the nuclear structure calculation to sd-shell configurations. Significant cancellations are observed between the different contributions to the effective three-nucleon force. The resulting three-body matrix elements yield only a small influence on the spectrum of the A = 19 systems. The typical size of the matrix elements, however, is large enough to expect a serious influence on the results of shell-model calculations with more than three valence nucleons.     

Three-body forces and4He

Some two-pion exchange three-body forces are examined as effective two-body potentials in the framework of exp(S) many-body theory. Each effective potential is added to the Reid soft core potential and a fully self-consistent calculation carried out. The most reasonable three-body forces give remarkably good agreement with experiment.     

Three-body forces in the lattice dynamics of some hcp metals

The consideration of paired interionic forces cannot explain the lattice dynamics of Be, Tb and Ho. In the present work, a phenomenological force constant model has been developed which considers three-body forces in addition to the usual forces of paired character. This approach explains the correct ordering of dispersion branches and the experimental degeneracy of the K-point in Be, Tb and Ho. Further good agreement is found between the theoretical curves and the neutron data of three high symmetry directions $\text{[0001], [01}\text{1}\text{0] and [11}\text{2}\text{0]}$ for all the three hcp metals.     

Computation of some thermodynamics, transport, structural properties, and new equation of state for fluid methane using two-body and three-body intermolecular potentials from molecular dynamics simulation

Molecular dynamics simulation has been performed to obtain pressure, radial distribution function, and self-diffusion coefficient of fluid methane using one site OPLS (optimized potentials for liquid simulations), five sites OPLS-SITE, and two-body HFD (Hartree-Fock dispersion)-like potentials. To take higher-body forces into account, three-body potential of Hauschild and Prausnitz (1993) has been used with the two-body HFD-like potential. The significance of this work is that the three-body potential of Hauschild and Prausnitz extended as a function of density and temperature and used with the HFD-like potential to improve the prediction of the results of pressure of fluid methane without requiring an expensive three-body calculation. The molecular dynamics simulation of methane has been also used to determine a new equation of state. The results are in a good agreement with experimental and theoretical values.     

The asymptotic D-state to S-state ratio of triton

At low energies, an effective field theory (EFT) with only contact interactions as well as three-body forces allow a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behaviour. Triton as a three-body system, based on the EFT have been previously shown to provide representative binding energies, charge radii, S-wave scattering amplitude and asymptotic normalization constants for the ³H bound state system. Herein, EFT predictions of the asymptotic D-state to S-state ratio of triton are calculated to more fully evaluate the adequacy of the EFT model. Manifestly model-independent calculations can be carried out to high orders, leading to high precision.     

Form factor dependence of proton induced deuteron breakup at low energy

Proton induced deuteron breakup has been studied experimentally and theoretically. The precision of the data makes it possible to distinguish between calculations made with different separable two-body forces. The possibility to observe off-shell effects and three-body forces is discussed.     

A new type of disconnectedness problem in a field-theory model of the NNπ system

When treated as an effective three-body problem in the framework of a simple field-theory model, the NNπ system acquires, in addition to the disconnected subsystem interactions usually considered, a new type of disconnected driving term, possible only for non-conserved particles such as the π. These terms pose a disconnectedness problem more intricate than that solved by Faddeev's equations or their known modifications for connected three-body forces. The solution of this problem in terms of a set of connected-kernel integral equations is presented.     

Ab initio shell model calculations with three-body effective interactions for p-shell nuclei

We present a qualitative improvement of the ab initio no-core shell model (NCSM) approach by implementing three-body interaction capability for p-shell nuclei. We report the first calculations using three-body effective interactions derived from realistic nucleon-nucleon potentials for 6Li, 8Be, and 10B and demonstrate that the use of three-body effective interactions speeds up the convergence of the NCSM approach. For 10B, we predict JpiT = 1(+)0 ground state, contrary to the experimental observation of 3(+)0, when the AV8(') potential is used, indicating the need for true three-body forces.     

Neutron Resonance States in Overdense Crystals

New three-body resonances appeared in the neutron scattering on two nuclei fixed in nodes of overdense crystalline lattice have been calculated for the iron group isotopes. These resonances are strongly dependent on the lattice parameters and characteristics of two-body resonances in neutron–nucleus subsystems. The effective forces created by the neutron resonance rescatterings supplement the Coulomb forces between nuclei of the crystalline lattice. These effective resonance interactions occur only at certain distances between nuclei and are accompanied by gamma radiation.     

热核物质中基态关联修正下的单核子势和核子有效质量

以有限温度Brueckner-Hartree-Fock(BHF)方法为基础，利用质量算子的空穴线展开，计算了不同温度和密度下的核物质中单核子势和核子有效质量，特别是研究和讨论了基态关联效应和三体核力贡献对热核物质中单核子势的影响. 研究表明，基态关联和三体核力对单核子势的密度和温度依赖性均有重要影响. 基态关联导致的重排修正具有排斥性，大大减弱了低动量区域单核子势的吸引性，而且基态关联效应对单核子势的贡献随密度增大而增强，随温度升高而减弱. 三体核力对基态关联的影响是导致单核子势中重排项贡献减小. 在高密 关键词： 有限温度BHF方法 质量算子空穴线展开 重排修正 单核子势 有效质量     

On the sensitivity of n-d scattering states to the nucleon-nucleon interaction

A new set of separable P-wave interactions and rank-2 tensor forces have been constructed and applied in three-body calculations for n-d elastic scattering at E_{n = 22.7 MeV}. A significant sensitivity of the polarizations to the different tensor forces and to the ³D₂ interaction has been found.     

Three-body forces and many-body dynamics

Conventional many-body quantum theory considers, as a rule, a system of particles in the mean field interacting through two-body forces. Recently it was suggested that in nuclear physics many-body forces, first of all three-body ones, are important for saturation of nuclear matter and for many details of nuclear structure. We consider possible influence of three-body forces, regardless of their origin (bare nucleon interactions or effective medium phenomena), on many-body dynamics. The new effects include, but are not limited to, renormalization of pairing and other two-body forces, enhancement of anharmonicity for collective modes, and special features of shell model calculations. The text was submitted by the author in English.     

Role of nonpair forces in the lattice dynamics of h.c.p. metals

Summary An analysis of the role of the nonpair forces in the lattice dynamics of s.p. bonded h.c.p. metalsviz. Mg and Zn has been presented. The total energy has been extended up to third order in the electron-ion pseudopotential. The dynamical matrix contains the terms arising from central pairwise interactions between the ions as well as contributions due to sums of nonpair three-body forces. Such forces, arising from the inclusion of third-order terms, are of short-range nature and possess the character of tensor forces. It is concluded that the nonpair three-body interaction is necessary for explaining the lattice dynamics of h.c.p. metals. The theoretical dispersion curves are compared with the experimental data. Good agreement is found between the computed and experimental results along the symmetry directions.

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Riassunto Si è presentata un’analisi del ruolo delle forze non appaiate nella dinamica reticolare di metalli h.c.p. limitati da s.p. rispetto a Mg e Zn. L’energia totale è stata estesa fino al terz’ordine nel potenziale elettrone-ione. La matrice dinamica contiene termini che originano da interazioni del tipo a coppie tra ioni cosiccome contributi dovuti a somme di forze a tre corpi non accoppiati. Tali forze, che derivano dall’inclusione di termini di terz’ordine, sono del tipo a corto raggio e possiedono le caratteristiche di forze tensoriali. Si conclude che l’interazione a tre corpi non appaiata è necessaria per spiegare la dinamica reticolare di metalli h.c.p. Le curve teoriche di dispersione sono confrontate coi dati sperimentali. Si è trovato un buon accordo tra i risultati teorici e sperimentali lungo le direzioni di simmetria.

     

Model Study of Three-Body Forces in the Three-Body Bound State

The Faddeev equation for the three-body bound state with two- and three-body forces is solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar two-meson exchange three-body forces. For two- and three- body forces of ranges and strengths typical of nuclear forces the single-particle momentum distribution and the two-body correlation function are similar to the ones found for realistic nuclear forces.     

Study of high-pressure phase transition of CeTe and EuTe through three-body interaction potential approach

The high pressure phase transition of lanthanum monotellurides having NaCl-type (B₁) structure have been studied using three-body interaction potential (TBIP) approach. The potential model consists of long-range Coulombic, three-body interaction forces, short-range overlap repulsive forces operative up to next nearest neighbor ions, van der Walls interactions and zero point energy effects. To understand the effect of pressure on elastic constant and their combinations, they have also been studied. The Born stability criterion was also found to be fulfiled in the present study. Our calculated results of phase transitions, volume collapses and elastic behavior of these monotellurides are found to be close to the experimental results. This shows that the inclusion of three-body interaction effects makes the present model suitable for high-pressure studies.     

Discussion on Weakly Bound States of Three-Body Systems

The equivalent two-body method for a three-body system has been generalized to an arbitrary three-body system with short-range two-body interactions. An analytical expression for the long-range effective potential is obtained for the Gaussian potential, the Yukawa potential and the exponential potential. The asymptotic behavior of the effective potential at very large distance is found to be universal and an explanation on the significance of universality is given. The weakly bound excited state for the system is first obtained although there is no bound state for two-body subsystems.